Bruno Chevillon was born in Valréas, in the Vaucluse, on August 23, 1959. He trained in two directions at once: he graduated from the Beaux-Arts in 1983, where he studied photography, and he took classical double bass lessons with Joseph Fabre at the conservatoire in Avignon. According to a biography published by the Conservatoire de Paris, he joined the saxophonist André Jaume's jazz class in 1982 and gave his first concerts among the Marseille musicians around Jaume, then moved closer to the improvisers' collective GRIM and the guitarist Jean-Marc Montera. His first records date from that period, among them Jaume's Musique pour 3 & 8: Errance (Hat Hut, 1984) and the Thierry Maucci Quartet's Elogio dell'Ombra (GRIM Musiques, 1986).

The decisive encounter, according to the same biography, was with Louis Sclavis in 1985, through the Lyon collective ARFI. Chevillon is on the ARFI record Sept jeunes et fiers maris by Le Marvelous Band (1985) and went on to follow Sclavis through most of his projects: the septet record Chamber Music (IDA, 1989), the sextet and quintet dates of the early 1990s, the Acoustic Quartet that Sclavis co-led with the violinist Dominique Pifarély (ECM, 1994, with Marc Ducret), and, in 2001, the quintet of L'Affrontement des prétendants. In 1989 he also formed a trio with the trombonist Yves Robert and the American drummer Aaron Scott, which recorded Des satellites avec des traces de plumes (Evidence, 1990). In 1994 Michel Portal noticed him, and he later played in Portal's quartet with the pianist Bojan Z. He is credited on Portal's sextet record Dockings (1998) and on the quintet album MP85 (Label Bleu, 2021).

From the second half of the 1990s he built a set of lasting partnerships with other improvisers. With the pianist Stephan Oliva he made Jade Visions, a programme drawn from the repertoire of Bill Evans, and then, with the drummer Paul Motian, two records of Motian's compositions, Fantasm (2000) and Intérieur nuit (2001). He joined the trios of the pianist François Raulin and of Daniel Humair with Ducret, which became a quartet with the tenor saxophonist Ellery Eskelin on Liberté surveillée (2001), and played in Ducret's trio with the drummer Éric Échampard, which recorded L'Ombra di Verdi (Screwgun, 1999). Duo records followed, with the clarinettist Jean-Marc Foltz (Cette opacité, Clean Feed, 2005) and with Tim Berne (Old and Unwise, Clean Feed, 2011).

Alongside jazz he has worked in contemporary music, dance and theatre. In 2001 he created Canicule for double bass and sampler with the composer Samuel Sighicelli at the Présences festival of Radio France, and the two founded the quartet Caravaggio with Benjamin de la Fuente and Éric Échampard, which has recorded several albums since 2005. He wrote and performed a solo recital based on poems by Pier Paolo Pasolini, and the Conservatoire de Paris biography lists a 1991 dance piece, Face Nord, with the choreographer Mathilde Monnier, and a project with the photographer Guy Le Querrec. His solo album Hors-Champ (d'Autres Cordes, 2007) combines double bass with electronics and the voice of Antye Greie-Fuchs on two tracks. In 2014 he became artistic adviser of the Orchestre national de jazz alongside the guitarist Olivier Benoit, and plays double bass and electric bass on the ONJ albums Europa Paris (2014) and Europa Berlin (2015).

In February 2023 the Conservatoire de Paris invited him to direct a session with its class in generative improvisation. His recent work includes the trio album Nautiles with the guitarist Philippe Mouratoglou and the drummer Ramón López (Vision Fugitive, 2025) and a second solo album, États des lieux (Songs, 2026).

Chevillon is a bassist of the improvised and avant-garde scene who treats the instrument as a source of sound material as well as of lines. A Conservatoire de Paris biography describes him as working at the borders of improvised music, contemporary composition and free jazz, an accompanist with a decisive presence and a soloist who explores the instrument's expressive range, with bow technique, mallets, prepared strings and percussion, and sometimes his own voice. The same text places him in the line of French bass improvisers that runs through Jean-François Jenny-Clark, Joëlle Léandre and Barre Phillips, and names Scott LaFaro and Gary Peacock as early marks on his playing. English Wikipedia calls him mainly a sideman who also flourishes as a soloist, and All About Jazz describes his approach to the double bass as sculptural and conceptual. The same biography suggests that his training in photography and the plastic arts carries into his attention to sound material, gesture and the physical relation to the instrument.

His catalogue ranges from the chamber-jazz interplay of the Louis Sclavis quartets and the Oliva and Paul Motian trio to free improvisation with Tim Berne and Foltz, electronics (Hors-Champ, Caravaggio) and the Orchestre national de jazz's Europa programme. His work sits closest to avant-garde jazz and European free jazz.